This is why the US system sucks - in the UK I get 4 weeks fully paid sick leave from my employer, and after that a further year of statutory sick pay from the Government. I also get 5 weeks paid holiday against which my sick leave does not count. In addition, I get reasonable accommodation to go see the doctor, dentist, optician, hospital etc etc.
Why is the "land of the free" not similar?
Because, due to history, mainly WW2, vacation as well as sick days and health care have mostly been relegated to the employers rather than by the government. Easy explanation is that it happened because during WW2, there was a pay freeze mandated due to the war effort, so employers started offering healthcare,sickdays, and vacation, above and beyond any required by law, as part of the job offer because that's what they could offer to get new employees in a time of a labor shortage. This continued after the war as it was now a standard part of employment. Thus, the middle class was largely taken care of and there was no large push to get the government involved. The cultural expectation is that if you want better of any of these things, you should get a better job which should just require work on your part. Also coming from that, is the cultural expectation that if you don't have better that what the law demands employers give you, that you are a slacker.
I have it pretty good in the US and get two and half weeks a year of sick time (which carries over from year to year, so at this time, I actually have about five months of sick time since I hardly ever use it) and after ten years, five weeks of vacation time a year (which also carried over). I'm happy where I'm at because while I could probably find a job that pays more, I probably couldn't find one that gave me as much vacation time which is now in higher demand to me than more money.